LANS Informal Seminar: Frank Giraldo

Seminar Title: The Galerkin Numerical Modeling Environment (GNuMe), Part II: Numerical and High-Performance Computing Details
Speaker: Frank Giraldo, Professor of Applied Mathematics, Naval Postgraduate School

Date/Time: 2017-06-28 11:00
Location: Bldg. 240, 4301

Description:
In this talk, I will dig deeper into the details of the GNuMe framework. In particular, I will discuss the spatial discretization methods used in GNuMe, i.e., spectral element and discontinuous Galerkin methods and how we have been able to write a unified discretization of these methods. A discussion on our approach for using adaptive mesh refinement (AMR)within GNuMe will also be included and how this could be used successfully in many geophysical fluid dynamics simulations. GNuMe also contains a modest collection of time-integration methods in order to advance the equations forward in time. For example, GNuMe contains both multi-step and multi-stage time-integrators including explicit, fully-implicit, and implicit-explicit methods. The scalability of these methods on large core-count computers will also be discussed including results obtained on the ALCF Mira and OLCF Titan. Our approach to accessing manycore architectures has been through a hardware-agnostic approach which allows us to write our compute kernels once and then compiling on each specific hardware at run-time. Although GNuMe contains a modest collection of iterative solvers (GMRES, BiCGStab, Richardson Extrapolation), it only contains a few preconditioners which we need to rectify in the next few years.